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Lifelong learning remains an open problem. One of its main difficulties is catastrophic forgetting. Many dynamic expansion approaches have been proposed to address this problem, but they all use homogeneous models of predefined structure for all tasks. The common original model and expansion structures ignore the requirement of different model structures on different tasks, which leads to a less compact model for multiple tasks and causes the model size to increase rapidly as the number of tasks increases. Moreover, they can not perform best on all tasks. To solve those problems, in this paper, we propose a new lifelong learning framework named Searchable Extension Units (SEU) by introducing Neural Architecture Search into lifelong learning, which breaks down the need for a predefined original model and searches for specific extension units for different tasks, without compromising the performance of the model on different tasks. Our approach can obtain a much more compact model without catastrophic forgetting. The experimental results on the PMNIST, the split CIFAR10 dataset, the split CIFAR100 dataset, and the Mixture dataset empirically prove that our method can achieve higher accuracy with much smaller model, whose size is about 25-33 percentage of that of the state-of-the-art methods.